Exact Charge Dynamics in the Supersymmetric t-J Model with Inverse-Square Interaction

Dynamical charge structure factor $N(Q,\omega)$ with $Q$ smaller than the Fermi wave number is derived analytically for the one-dimensional supersymmetric t-J model with $1/r^2$ interaction. Strong spin-charge separation in dynamics is found. $N(Q,\omega)$ with given electron density does not depend on the spin polarization for arbitrary size of the system. In the thermodynamic limit, only two holons and one antiholon contribute to $N(Q,\omega)$. These results together with generalized ones for the SU($K$,1) supersymmetric t-J model are derived via solution of the Sutherland model in the strong coupling limit.